In the graduation scene, the cable to the loan shark's earphone changes position between shots.
During the poker game, Lawrence's cigarette changes back & forth from half smoked to unlit.
The Peace Corps plane changes from a prop plane to a jet between shots.
During the poker game, Lawrence throws all his money into the pot, but when he looks at his hold card he still has money next to it.
During the Commencement Ceremony, Lawrence is listening to Game 7 of the 1962 NBA Championship. While the score is correct (Celtics 110, Lakers 107), the scene takes place in the afternoon. The game was played on a Wednesday night.
Early in the movie, after Lawrence boards the airliner and the cabin door is shut, one of the thugs chasing him tries to board the plane by jumping from the stairway. When he hits the side of the plane, the cabin door flexes and moves, revealing it to be a fake door.
When John Candy's character encounters a tiger in the jungle, the tiger has no teeth. It was a circus tiger used for tricks and has no teeth or claws.
On their flight to Lung Taho they are using a Bell 212 (a twin turbine version of the military Bell 202/Huey 1a). Bell did not start manufacturing the Bell 212 (known in military service as the Huey 1d) until 1967. The first models where not shipped till 1968. The movie is set in 1962.
On the plane, the Peace Corp volunteers are singing "Puff, the Magic Dragon" in 1962. Peter, Paul and Mary recorded the song in 1962 and it wasn't released until 1963.
In the scene in the bar when Beth asks for a Coke, Lawrence pulls a couple of then-current era--1985 - Coca-Cola bottles out of the cooler. The 1985 Coke bottle had a slimmer, straighter shape than the era-correct (1962), green wasp-waist Coke bottle, with a red block logo with "Coca Cola" in white script.
During the climatic scene on the bridge, Lawrence is able to distract John by pretending to hear the sound of a Russian MiG-25 fighter jet. While the movie is set in 1962, the first prototype MiG-25 did not fly until 1964 and the aircraft did not enter service until 1970.
When Bootsy Winder is in Lawrence's room on the day of graduation, she announces that she must leave immediately because she is giving the valedictorian speech that morning at Smith College. However, Smith College is 90 minutes away from Yale.